Security of algebraic curves in cryptography

对于给定的安全级别，椭圆曲线加密（ECC）和超椭圆曲线加密等一般化代表了目前可用的最有效实现的公钥加密系统。所有其他公钥密码系统，如RSA (Rivest-Shamir-Adleman)，要么承认次指数时间攻击，要么没有在足够长的时间内受到相同级别的审查，以保证对其安全性的信心。因此，在国际标准中，ECC被广泛采用为安全敏感或资源受限环境的首选密码系统。ECC的一个值得注意的应用是在移动电话的安全领域，在这个领域，较低的计算能力往往排除了使用效率较低的替代方案。

Elliptic curve cryptography (ECC) and generalizations such as hyperelliptic curve cryptography represent the most efficiently implementable public key cryptosystems available today for a given level of security. All other public key cryptosystems, such as RSA (Rivest-Shamir-Adleman) either admit subexponential time attacks or have not been subjected to the same level of scrutiny for a sufficiently long period of time to warrant confidence in their security. For this reason, ECC has been widely adopted in international standards as the preferred cryptosystem for security sensitive or resource constrained environments. A notable application of ECC is in the area of security for mobile phones, where lower computational power often precludes the use of less efficient alternatives.